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Proof step 2 from proof cons-01 (previous step)

disj(x, y), a ∈ y, disj(a ' + x, y) ⊦

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ x, a. ¬(disj(x, y0) ∧ a ∈ y0 ∧ disj(a ' + x, y0)), disj(x, a0 + y0), a ∈ a0 + y0, disj(a ' + x, a0 + y0) ⊦

Rule argument

term: y

Additional information

Used simplifier rules: e: ⊦ disj(x, []);%list freely generated by [], +;;%in-empty: ⊦ ¬ a ∈ []; from specification list